A search for mode-selective chemistry: The unimolecular
dissociation of I-butyl hydroperoxide induced by
vibrational overtone excitation
David W. Chandler
Department o/Chemistry. Stanford University, Stanford, California 94305
William E. Farneth
Department o/Chemistry, University 0/ Minnesota, Minneapolis. Minnesota 55455
Richard N. Zare
Department 0/ Chemistry. Stanford University, Stanford, California 94305
(Received 6 July 1982; accepted 22 July 1982)
The use of optoacoustic spectroscopy permits both the monitoring of the overtone excitation of tbutylhydroperoxide (t·BuOOH) and the in situ detection of the resulting reaction product t-butanol (tBuOH). The sample is contained in a reaction cell, equipped with a microphone, in which all surfaces have
been specially passivated. The cell is placed inside the cavity of a dye laser tuned to excite the 5-0 O-H stretch
of the t-BuOOH at 619.0 nm. The dissociation process yields directly ·OH and t-BuO·, and the latter readily
abstracts a hydrogen atom from a parent molecule to form t-butanol (t-BuOH). The appearance rate of tBuOH is obtained by ratioing the area under the 5-0 O-H stretch of t-BuOH to that of a combination band of
t-BuOOH. At low pressures, below 40 Torr, a plot of the reciprocal of the t-BuOH appearance rate versus
total pressure shows near linear behavior. This linearlity can be well described by a statistical model (RRKM)
when careful averaging of the dissociation rate over the thermal energy distribution of the photoactivated
molecules is included. At pressures above 40 Torr, a marked deviation from linearity appears. This deviation
is fit to a kinetic model in which the dissociation rate of an energy nonrandomized molecule competes with
the rate of intramolecular energy relaxation. This places a lower bound of ~ 5.0 X 10" S -Ion the rate of
energy randomization. A discussion of this model in the context of other possible kinetic schemes as well as
other photoactivated and chemically activated systems is presented.
I. INTRODUCTION
One of the most provocative questions in chemical
dynamics over the last three decades has been the range
of validity of ergodic theories of unimolecular reaction.
The history of experiments that deal with this question
began with attempts in the 1950's and 1960's to distinguish experimentally between statistical (RRKM) and
nonstatistical (Slater) theories of thermal unimolecular
processes. 1 The ergodic theories were very successful
in rationaliZing the bulk of this data. 2 More recent work
has concentrated on chemical3 and photochemical, 4,5
rather than thermal activation methods. A driving force
for this continuing investigation is the presumption that
given a sufficiently selective activation method and a
sufficiently short reaction timescale, deviations from
ergodic behavior must become apparent.
Among the most elegant work in this field is that of
Rabinovitch and co-workers. 3 In a series of experiments which has extended over most of the three-decade
history of this field, this group established and validated
an experimental procedure for determining the relative
rates of nonstatistical reaction and intramolecular relaxation. In these experiments selective excitation of
a molecule is achieved by means of chemical activation.
This excitation mechanism consists of the addition of a
radical to a stable molecule producing a quasistable
molecule which unimolecularly dissociates with a characteristic rate. The excess chemical energy released
through the addition process is initially localized at the
site of the addition. The rate of intramolecular relaxation of this initial localized energy is the quantity of inJ. Chern. Phys. 77(9). 1 Nov. 1982
terest. To determine this rate the decomposition rate
is studied as a function of pressure. As the pressure is
increased the rate of collisional stabilization competes
with dissociation. Plots of decomposition rate versuS
pressure give insight into the rate of intramolecular energy relaxation. These plots may be either linear or
curved.
Linearity is the expected result of reaction exclusively from an energy-randomized reactant. Curvature can be understood based on a model that permits
some reaction to occur from a distribution of the internal energy over only a subset of the total phase space.
Whether this nonrandom component is observable or not
depends on the structural relationship between the site
of energy deposition by the activating reaction and the
reaction coordinate for unimolecular decay.
These concepts are perhaps best illustrated by the
unimolecular decomposition of the adduct formed in the
reaction of methylene with neopentyl cyclobutane (see
Fig. 1).6 Two of the possible "hot" products that result
depending upon whether CH2 inserts into a C-H bond of
the ring or the alky I chain are shown as path "a" and
path "b, " respectively. The pressure dependence of
the rate of product formation via path a is curved while
that of path b is linear. Ko and Rabinovitch 6 interpret
this data to indicate that deposition of energy into the
ring by path a causes cyclobutane ring cleavage to be
sufficiently fast to compete with energy randomization.
For path b this is not the case because excitation by
path b is remote from the reaction center, and no decomposition can ensue until randomization has occurred,
021-9606/82/214447-12$02.10
© 1982 American Institute of Physics
4447
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4448
Chandler, Farneth, and Zare: Mode-selective chemistry
H
"C='C H
/
H/
'H
+
CH 3
CH
I
I 3
CH = C-CH -C-CH
2
2
I
3
CH 3
FIG. 1. Chemical activation experiment of Ko and Rabinovitch (Ref. 6) showing competing decay channels in CH 2 : neopentyl
cyclobutane. Path "a" (energy deposition on the ring) displays nonergodic behavior at high pressure. Path "b" (energy deposition
on the chain) does not.
Similar studies have been carried out by Rabinovitch
and co-workers on fluoroalkylcyclopropanes, 7 alkylcyclobutanes,8 and hexenes. 9 In all cases the adduct contains excitation much in excess of the activation energy
for decomposition. Moreover, the efficiency of intermode energy coupling is expected to increase rapidly
with increasing excitation, and the chemical activation
method does not prepare a narrow distribution of adduct
energy states.
Aside from these experiments, there are very few
examples in unimolecular dynamics of polyatomics activated by any method that cannot be adequately rationalized using statistical theory and presuming ergodic behavior. Of particular pertinence to this work is the
study by Reddy and Berryl0 on the pressure dependence
of the isomerization rate of allyl isocyanide activated by
Single-photon absorption to a high-lying vibrational
overtone. While the pressure behavior was linear the
dissociation rates extracted from the data were not in
uniform agreement with calculated RRKM rates. It was
inferred that the process was nonergodic from the observation of nonmonotonic energy dependence of the unimolecular rate constants resulting from excitation into
overtone bands of different C-H stretches.
The experiment which we wish to report utilizes overtone pumping to initiate unimolecular reaction in a molecule specifically chosen to mimic the behavior of the
chemical activation systems. Tert-butylhydroperoxide
(t-BuOOH) possesses a number of features which make
it attractive for experiments of this kind:
(1) It contains both O-H and C-H oscillators. Because of the high frequency and anharmonicity of these
local modes, 11 they might both be expected to have reasonable intensity in ~v = 5, 6 as is required to exceed
the threshold energy for decomposition (43 kcal/mol).12
(2) It has a low energy reaction pathway that involves
a simple reaction coordinate. The Arrhenius parameters for (CH3hCOOH- (CH3)3CO. +. OH have been well
documented. 13
(3) The bulk of the vibrational state density involves
displacements of the hydrocarbon portion of the molecule. Excitation of the O-H stretching overtone initially deposits energy remote from this energy sink and
separated from it by the 0-0 bond. Therefore, as in
the Rabinovitch experiments, the competition between
nonergodic reaction and intramolecular relaxation may
be different for excitation into pure O-H, C-H, or combination band overtones.
Our experiments are carried out using an intracavity
optoacoustic cell for both spectroscopy14-16 and photochemistry. Overtone pumping of the reactant t-BuOOH
initiates the chemistry, and overtone probing of the
O-H transition of the product t-butyl alcohol (t-BuOH)
is used to monitor the rate of product formation. These
techniques allow the reaction to be followed continuously
and nondisruptively.
J. Chern. Phys., Vol. 77, No.9, 1 November 1982
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Chandler, Farneth, and Zare: Mode"selective chemistry
4449
BIREFRINGENT
FIL TER
REACTION CELL
TOTAL
REFLECTOR
ION LAS E R
P:-:·Z;:·:·:·TI.:···TI··=m.t:TITITI=mTITI§ill~.
LIGHT
CHOPPER
,--_ _ _-, LOCK-IN
PHOTODIODE
STRIPCHART
RECORDER
FIG. 2. Experimental setup (see the text).
II. EXPERIMENTAL APPARATUS
The quantitative detection of t-BuOOH and its photolysis product t-BuOH requires the use of special procedures because of the heterogeneous decomposition of tBuOOH to form t-BuOH on glass and metal surfaces.
As a consequence, conventional GC is ruled out. Moreover, spectroscopic techniques, such as FTIR, prove
awkward because of gas handling problems. Instead,
in situ detection of t-BuOOH and t-BuOH is carried out
by observing the optoacoustic Signal arising from overtone absorptions of both compounds. In this method,
absorption results in a pressure change which is detected by a microphone placed inside the cell. This permits direct measurement of the concentration ratio
[t-BuOH]![t-BuOOH] during the course of photolysis.
Figure 2 is a schematic diagram of the apparatus.
An argon ion laser (Coherent Model CR1B), modulated
at 500-BOO Hz, pumps a homebuilt linear dye laser 17
operating with rhodamine in ethylene glycol. The wavelength of the dye laser is scanned by means of a motordriven three-plate birefringent filter (Coherent Radiation) affording a resolution of - 2 cm- 1 • Power in the
cavity is monitored by a photodiode from a reflection off
the birefringent filter through a polarizer. The intracavity power varies between 40 and 120 Was the pump
laser varies from 4-15 W (all green lines). An intracavity laser power of 40 W corresponds to - 6 mV photodiode signal. The intracavity power measurements are
calibrated by using the known transmittance of the back
mirror of the cavity. Both the optoacoustic signal from
the microphone and the Signal from the photodiode are
processed by lock-in amplifiers (PAR Model 163). The
lock-in outputs are ratioed before the optoacoustic spectrum is displayed on a stripchart recorder.
The reaction cell is placed inside the dye laser cavity.
It is equipped with a 1 in. condenser-type microphone
(Bruel and Kjael Model 4144). The optoacoustic reaction cell is constructed so that t-BuOOH can be maintained for extended periods of time without significant
decomposition. This is accomplished as follows: First,
the pyrex walls of the cell are coated with fluorocarbon
polymer. 18 A mixture of hexafluoropropylene (300
Torr) and di-t-butylperoxide (20 Torr) is heated to
2BO °C for 10 h inside the cell. After this treatment,
the cell walls appear slightly opaque and water poured
into the cell shows no miniscus. Second, the microphone face is painted with fluorocarbon wax19 dissolved
in a small amount of acetone. The microphone is placed
in the cell so that only its face is exposed. Next the
teflon-coated windows are removed and a mixture of 5%
F2 in Ar is passed through the cell for 48 h. New quartz
windows are attached using epoxy (Torr Seal) and the
cell is evacuated while being baked at 70°C. After outgasing has ceased (about 1 week), the reaction vessel is
filled with t-BuOOH (7 Torr) and "seasoned" for 24 h.
This last step is repeated seven times. FollOwing this
treatment on the order of 1% of the t-BuOOH is converted to t-BuOH by wall reaction during a 12 h period.
Exposure to ambient room light has no effect on this
background rate of decomposition.
Samples of t-BuOOH (Lucidol Pennwalt) are vacuum
distilled over magnesium sulphate. Less than 2% of
t-BuOH is present after distillation, as determined by
gas-phase infrared absorption measurements.
J. Chem. Phys., Vol. 77, No.9, 1 November 1982
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4450
Chandler, Farneth, and Zare: Mode-selective chemistry
614.4
519.5 nm is also observed.
609.6
For t-BuOH Fig. 3 shows the 5-0 tranSition of the
O-H stretch at 606.4 nm, while the 6-0 transition is
observed to occur at 519.0 nm. Both of these bands
show the characteristic "P, Q, R" prOfile of the t-BuOH
O-H fundamental. They belong to a progression whose
transition energies are reproduced by Eq. (1) with
A=3725 and B=-85.3 cm- t •
8
'"Eo
Sharp lines also appear in the optoacoustic spectrum
(see Fig. 3) but are readily identified as cOming from
water vapor. Water is present in the prephotolyzed
sample and is also a product of the photolYSis. Fortunately, these lines do not interfere with the bands of
t-BuOOH or those of t-BuOH used to quantify the latter.
Table I summarizes the spectral assignments.
x
b
FIG. 3. Visible overtone spectrum of 7 Torr t-BuOOH plus
0.5 Torr t-BuOH. Absolute cross sections were obtained by
comparison with C-H overtone absorption strengths of benzene. The top trace is the optogal vanic spectrum of Ne used
for calibraUon purposes.
Figure 3 shows a typical spectrum of t-BuOOH and tBuOH in the 600-630 nm region. Peaks are assigned
based on their positions, profiles, and strengths. For
t-BuOOH the band at 619.0 nm is identified as the 5-0
transition (fourth overtone) of the O-H stretch. The
4-0 and 6-0 tranSitions at 751. 0 and 531. 9 nm can also
be observed using the present experimental setup. The
v-O transition energies of the O-H stretch are given by
the reiation20
=v(A + vB)
the signal strength from benzene vapor, using the previously reported absolute absorption cross sections for
the C - H overtones of the latter. 22
IV. ANALYSIS OF KINETIC DATA
III. OVERTONE SPECTRA
E,,-O
Absolute absorption cross sections for t-BuOOH and
t-BuOH overtones are determined by comparison with
(1)
,
where the constants A and B have the values 3692 and
- 92. 2 cm-1, respectively. A similar v-O progression
arises for overtones of the C - H stretch and leads to
the assignment of the broad peak at 625.0 nm to the 6-0
transition (fifth overtone). A very broad and weak feature centered near 549.0 nm is also observed and assigned to the next member (sixth overtone) of this progression. The fourth overtone of this progression is
partially obscured by a strong OH combination band but
seems to be centered around 736.5 nm. These assignments can be fit to Eq. (1) with A = 2985 and B = - 53.1
cm -1. As further support for these assignments, the
0- H overtones are strong and unstructured while the
C-H overtones in the same spectral region are much
less intense corresponding to their higher overtone
number. Furthermore, the C-H overtones have an
asymmetric profile.
In addition, broad bands appear 260 ± 20 cm- 1 to the
blue of the O-H stretching overtone in the same wavelength region. An example is the feature centered at
609.5 nm in Fig. 3. This progression is assigned to
combination bands consisting of v quanta of the O-H
stretch plus one quantum of a skeletal bending mode,
most probably the C-O-O bend having a fundamental
frequency of - 270 cm- t • 2t The feature at 603.0 nm is
another combination band likely involving one quantum
of a different skeletal mode. A companion feature at
Overtone spectra are taken before and after a period
of irradiation, usually 1 h. Typical pre- and post-photolysis spectra are shown in Fig. 4. The rate of tBuOH production is determined by ratioing the difference
in the area of the t-BuOH 5-0 O-H stretch at 606.4 nm
in the pre- and post-photolyzed spectra to the area of the
t-BuOOH O-H combination band at 609.5 nm. The photolysis rate is found to vary with gas pressure, laser
wavelength, and laser power.
Baselines for the spectra are drawn by hand. Areas
are measured with a planimeter and in any given run the
[t-BuOH]I1t-BuOOH] ratio is reproducible to within 10%.
Because the total conversion of t-BuOOH to t-BuOH is
typically less than 2% between measurements, the value
of [t-BuOOH] is treated as constant in calculation of the
ratio. However, the t-BuOH produced from the back-
TABLE I. Observed overtone features in a mixture of t-BuOOH
andt-BuOH.
Wavelength (nm)
Assignment
t-BuOOH
751. 0
736.5
738.1
4-0 O-H stretch
5-0 C-H stretch
4-0 0-H stretch + 1-0 C-0-0 bend
619.0
625.0
609.5
603.0
5-0
6-0
5-0
5-0
0-H
C -H
0-H
O-H
stretch
stretch
stretch + 1-0 C-0-0 bend
stretch + ?
531.9
549.0
524.4
519.5
6-0
7-0
6-0
6-0
0-H
C-H
0-H
0-H
stretch
stretch
stretch + 1-0 C-O-O bend
stretch + ?
t-BuOH
606.4
519.0
5-0 0-H stretch
6-0 O-H stretch
J. Chern. Phys., Vol. 77, No.9, 1 November 1982
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Chandler, Farneth, and Zare: Mode-selective chemistry
4451
and is directly proportional to the photodiode signal
(units of mV), and T is the irradiation time (units of h).
At each pressure, kapp is obtained at several reaction
times and laser powers. Figure 6 displays this data in
the form of a Stern-Volmer plot where the reciprocal
of kapp is plotted against the total pressure in the reaction cell. No systematic variation is found at a given
total pressure with any of these variables. In particular, data at 1 Torr t-BuOOH and 159 Torr SFs (open
circle) and 7 Torr t-BuOOH and 153 Torr SFs (closed
circle) overlap within their uncertainties. The error
limits represent one standard deviation from the mean
at each pressure. In a few runs with other bath gases
(toluene or 1,4 cyclohexadiene), once more no obvious
change in k;';p is observed at a given total pressure.
Similarly, variation of laser power by a factor of 3
causes no change in the apparent rate constant outside
of experimental error limits. Irradiation at frequencies outside the overtone band profiles gives no reaction
above background.
after photolysis (3 hrs)
before photolysis
Figure 6 shows a near linear variation of k;';p with
pressure between 1 and 40 Torr. At higher total pressures k;';p deviates markedly from linearity and approaches a constant value corresponding to a t-BuOOH
photolysis rate 10% of the rate at 1 Torr (the lowest
pressure studied).
610
620
600 nm
FIG. 4. Overtone spectra before (lower trace) and after (upper trace) excitation of sample at 619.0 nm for 3 hr, with
~ 40 W of laser power. The 5-0 O-H stretch of t-BuOH,
marked by an arrow, is seen to grow in.
ground reaction cannot be neglected as seen in Fig. 5.
This figure demonstrates that in the passivated cell, at
typical laser powers and 7 Torr vapor pressure of tBuOOH, background reaction is less than 20% of the
light-induced reaction, and that furthermore, successive reaction or background periods give reproducible
product yields. At high pressures, corresponding to
low photolysis yields, the background reaction contributes significantly to the observed production of t-BuOH.
Consequently, the rate of dark reaction is determined
before and after each run. It is used to correct the apparent t-BuOH appearance rate to obtain the actual ratio
R of [t-BuOH] to [t-BuOOH] caused by photolysis according to the expression
R _ [t-BuOH]total -[t-BuOH]baCkgr9YPd
-
0.25
0.20
0.15
r~
o
m
I
0
0
m
~~
I
0.10
(2)
[t-BuOOH]
The total pressure in the reaction cell is varied from
1 Torr (the limit for observing the [t-BuOH]![t-BuOOH]
ratio by optoacoustic means) to 160 Torr. Between 1
and 7 Torr pure t-BuOOH is used while above 7 Torr
two types of experiments are performed. Sulfur hexafluoride gas is added to either 1 or 7 Torr of t-BuOOH.
Let kapp denote the normalized rate of appearance of
t-BuOH from t-BuOOH by overtone activation, i. e.,
k
Figure 7 shows complementary data taken by excitation of the t-BuOOH combination band at its peak (608.8
nm). The low-pressure slope mirrors that of Fig. 6.
However, the small amount of conversion to t-BuOH at
-~
(3)
app - [hV]T '
where [hv] is the photon density in the reaction cell,
0.05
0.000~~~~~10~~~-L~2LO~~-L~~3~0~~~~40
TIME (hrs)
FIG. 5. Plot of the ratio of area under 5-0 O-H stretch peak
of t-BuOH to area under 5-0 O-H stretch + 1-0 C-O-O bend
combination band of t-BuOOH as a function of time. The solid
line represents the laser on at frequency 619.0 nm and power
~ 35 W. The dashed line represents laser off and is a measurement of the background reaction.
J. Chem. Phys., Vol. 77, No.9, 1 November 1982
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Chandler, Farneth, and Zare: Mode-selective chemistry
4452
-
FIG. 6. Plot of the inverse of the rate
of t-BuOH appearance (k~) vs total
pressure for excitation at 619.0 nm .
Below 7 Torr the experimental points
represent pure t-BuOOH. Above 7
Torr two types of experiments are performed, 7 Torr t-BuOOH + remainder
SFs (solid points) and 1 Torr t-BuOOH
+ remainder SF s (open points). The
open triangle at zero pressure is obtained by a calculation assuming each
absorbed photon causes dissociation
and no chain mechanism leading to tBuOH is present. The lines represent model calculations presented in
the text.
....
.r:
I
>
E
....Ie.
e.
III
.;,(.
80
PRESSURE
120
(torr)
higher pressures caused by the weaker absorption
strength of this combination band prevented accurate
determination of k;;p at these pressures. Consequently,
it was not possible to conclude whether k~!v deviates
from linearity at higher pressures for excitation of this
combination band.
V. DISCUSSION
A. Simple kinetic scheme based on statistical
decomposition of photoactivated t-BuOOH followed by
hydrogen abstraction
The following is a kinetic model that incorporates all
the elements of this experiment in the simplest possible
way:
Absorption (Rl) leads to an excited reactant molecule
t-BuOOHt, indistinguishable from the precursor to dissociation. The 0-0 bond cleavage (R2) occurs from
the vibrationally excited molecule in competition with
collisional quenching (R3). Tert-butyl alcohol is formed
by hydrogen abstraction from another molecule of peroxide (R4). The rate of t-BuOH formation is kinetically
equivalent to the rate of t-butoxyl radical formation.
At steady state this rate is given by
~[t-B OH] = k t k 2[hv][t-BuOOH]
kt
(Rl)
t-BuOOHt ~ t-BuO. +. OH ,
(R2)
ka
(R3)
M + t-BuOOIt - M + t-BuOOH ,
k2
+ k 3[M]
(4)
Reference to Eqs. (2) and (3) shows that
~[t-BuOH]
k
hv + t-BuOOH - t-BuOOIt ,
u
dt
app -
.r::-dt=--::-:----;r~
[t-BuOOH][hv]
_
kt k2
- k2 +k 3[M]
=ktP.
(5)
(R4)
Hence, kapp is, in effect, the rate constant for photoexcitation (k t ) times a pressure-dependent probability P
that an activated molecule will react, where
t-BuOOH +. OH - H2 0+t-BuOO. ,
(R5)
(6)
t-BuOO· ~ termination.
(R6)
k
t-BuOOH+t-BuO· :J t-BuOH+t-BuOO· ,
kS
This kinetic scheme predicts that a plot of k;;p versus
J. Chem. Phys., Vol. 77, No.9, 1 November 1982
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Chandler, Farneth, and Zare: Mode-selective chemistry
tween the predictions of this mechanism and the experimental results, values of ks!k2 as a function of [M] have
been calculated. ks is calculated assuming every collision of t-BuOO~ with [M] leads to deactivation (strong
collision assumption). Based on a hard sphere collision
diameter of 5 A, 2S the calculated value of ks is 8 x 106
s-t Torr-1 • RRKM theory has been used to calculate k2
as a function of internal energy (Fig. 8). For details of
the calculation see Appendix A. These calculations are
based on the well-established Arrhenius parameters for
t-BuOOH dissociation, and employ frequencies that are
essentially the same as those used in previous RRKM
calculations on peroxides. 24 The resulting values are
in excellent agreement with existing thermal25 and
photochemical5 rate data on t-BuOOH decomposition .
200
150
......
....
.l:
I
>
E
~
' ... 100
"'"
t
50
Also shown in Fig. 8 is the internal energy distribution function for the ensemble of t-BuOOH' excited at
619.0 nm. The corresponding function for excitation at
608.8 nm is identical but the origin is shifted by 270
cm-1 to higher energy. These distributions are calculated as the room temperature thermal distribution
j(E) =n(E)!no=g(E) exp(-E!kT) with the origin at the
photon energy. Here g(E) is the density of harmonic
oscillator states at energy E above the zero point energy
using the Stein and Rabinovitch algorithm26 ; use of this
distribution of excited molecules is equivalent to the
statement that the excitation of hot bands is statistical.
To the extent that this is not true the distribution is incorrect. If k2 is taken to be the RRKM rate constant
k(E) at the mean energy E of this distribution, then k2
=4x10' s-t.
+
00
40
80
PRESSURE
120
(torr)
160
FIG. 7. Plot of the inverse of the rate of t-BuOH appearance
(k~ vs pressure for excitation at 608.8 nm. The points rep-
resent 7 Torr t-BuOOH plus remainder SF 6 • The open triangle
at zero pressure is obtained by a calculation assuming each
absorbed photon causes dissociation and no chain mechanism
leading to t-BuOH is present. The large error bars at high
pressure result from the small amount of photolysis yield
above background.
total pressure [M] should yield a straight line with intercept kit and slope k s!(k t k 2).
The marked nonlinearity of the experimental data
makes it clear that this simple mechanism is inadequate.
To demonstrate the magnitude of the discrepancy be-
Assuming this mechanism fits the data at the lowest
pressure point (1 Torr), a "best fit" value for k t can be
determined from Eq. (5). This value of kt along with the
hard-sphere estimate of ks and the value of k 2(E) calculated above defines the slope of the plot of k~p vs [M]
predicted by the mechanism (R1)-(R6). In Fig. 6 this
prediction is shown as the dotted line. It obviously fails
to represent the experimental data at all pressures
above 1 Torr.
,
E
8
,....
•
6
•
•
•
•
W
---
C'I
..lI::
Cl
4
0
•
2
4453
•
FIG. 8. Plot of calculated dissociation rate (RRKM) of t-BuOOH as a
function of energy above threshold
(E 0) • The arrows on the energy axis
represent the energy of the photons
used (619.0 and 608. 8 nm). Superimposed upon the plot is a MaxwellBoltzmann population distribution for
t-BuOOH at room temperature (solid
line). The average is denoted by eE) •
Also superimposed is the reacting disdistribution peE ,£M) for a 1 Torr
pressure (dashed line).
J. Chern. Phys., Vol. 77, No.9, 1 November 1982
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Chandler, Farneth, and Zare: Mode-selective chemistry
4454
TABLE II. Chemistry of the tert-butoxyl radical at 300 K.
Reaction
(1) t-BuO. - / ~CO .... + . CH3
ABo
(kcal/mol)a
k(S'()b
Literature
source
+5.8
1 xI0 3
Reference 29
(2) t-BuO. +t-BuOOH-t-BuOH+t-BuOO.
-14
9 XIO'
References 30
and 31
(3) t-BuO. +t-BuOOH-t-BuOH+t-BuOOH
-6
3xIO(
References 30
and 31
7.8xlO'
References 30
and 36
(4) t-BUO·+O -t-BUOH+O
-30
aObtained from Ref. 31.
bFor bimolecular reactions 7 Torr of hydrogen atom donor was used. These rates are corrected
for the number of equivalent hydrogen atoms [i.e., 9 in (3) and 4 in (4)).
Simplifications of several types have been made in the
preceding analysis. These may be divided into four
areas: (1) the calculation of k 2; (2) the postdissociation
radical chemistry; (3) the assumptions about the nature
of the excited molecules; and (4) the possibility of contributions from other kinetic pathways. Each of these
are considered in an attempt to make the model more
realistic or justify its assumptions.
B. Average over the thermal distribution of
photoactivated t-BuOOH
Because of the finite spread in energies of t-BuooIf,
it is naive to identify k2 with k(It) where It is the mean
of the thermal energy distribution. As Fig. 8 shows,
k(E) changes too rapidly with E for this commonly-used
approximation to be valid. At a given pressure, molecules at the low end of the energy distribution are more
likely to be collisionally quenched than those at the high
end. Therefore, k~» must be calculated by integration
over the full energy distribution. That is, the probability to reaction is both E and [M] dependent:
_
_
k2(E)
P -P(E, [MJ) - k (E) + k [M] •
2
(7)
3
Then Eq. (5) becomes
ka»»
== k1
1.
E-hv
k2(E)
k 2(E) + k 3[M] j(E) dE ,
(8)
where j(E) is the energy distribution generated by photoexcitation (Fig. 8). As before, j(E) is taken to be a
Maxwell-Boltzmann distribution. USing k1 as a fitting
parameter as in Sec. A, but calculating k~» by numerical integration of Eq. (8) at each pressure gives the
dashed curve of Fig. 6. While this plot shows curvature in the appropriate direction within the experimental
pressure range, the curvature is clearly not sufficiently
large to fit the data. However, at the lowest pressure,
where the dashed line is fairly linear the slope is - 5
times smaller than that of the dotted line and gives fair
agreement with the low pressure data.
C. Postdissociation radical chemistry
Previous work on the thermal and photochemical production of t-BuO' from t-BuOOH has demonstrated that
unimolecular dissociation to acetone and . CH3 can compete with hydrogen abstraction R(4)27,28:
k7
t-BuO·-
>=0+' CH3
•
(R7)
The energy required for reaction (R7) could come from
the internal energy of the "hot" t-butoxyl radicals
formed in reaction (R2), or from collisional activation
of thermalized t-butoxyl radicals. However, no acetone
is observed by FTIR when a 7 Torr sample of t-BuOOH
is photolyzed at 619.0 nm. It is estimated that the yield
of acetone must be less than 5% of the t-BuOH yield.
The arguments below suggest that this is the expected
result.
The energy required for reaction (R7) is 5368 cm-1. 12
In other wordS, only t-BuOOHt with Et> Eo + 5368 cm- 1
have sufficient energy for acetone formation. Consequently, chemically activated formation of acetone
should be inSignificant given the energy distribution function of Fig. 8, the dispersal of energy that will accompany dissociation, and the additional energy above the
5368 cm- 1 threshold that will be necessary for reaction
(R7) to compete with collisional quenching.
Absolute first order rate constants for thermal reactions (R4) and (R7) calculated from the literature at
[t-BuOOH] == 1 Torr and T == 298 K are k7 == 1 X 103 s-129
and k4[t-BuOOH]=13.5xl03 S-1.30 Hence, the largest
ratio of acetone to t-BuOH expected in the present experiment is 7%. At pressures above 1 Torr this ratio
will decrease as reaction (R4) dominates reaction (R7)
with increaSing t-BuOOH concentration. The production
of acetone may contribute a small curvature to the low
pressure data of Figs. 6 and 7 but make insignificant
contribution above 7 Torr. The possible fates of the tBuO' radical are summarized in Table n for a pressure
of 7 Torr t-BuOOH.
While hydrogen abstraction from t-BuOOH appears to
be by far the most rapid reaction pathway available to
primary radicals, an additional complication is the possibility of secondary chemistry of the t-butylperoxyl
radicals t-BuOO' to form t-BuOH. A plausible route
from t-BuOO' to t-BuO' has been clearly defined in the
wealth of previous studies of t-BuOO' chemistry. 31 It
involves the formation and decay of a tetroxide in a radi-
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Chandler, Farneth, and Zare: Mode-selective chemistry
cal-radical reaction:
2t-BuOO' -~ [t-BuOOOOBu-t]- 2t-BuO, +02
•
(R8)
Reaction (R8) constitutes a propagation step in a radical
chain leading to t-BuOH. Whether such a chain occurs
or not depends on the likelihood of reaction (R8) relative to other possible fates of the t-BuOO· radicals. In
order for a radical chain to rationalize the turnover at
high pressure in Fig. 6, the chain length must increase
with increasing pressure. If the radical chain length
were independent of pressure, its presence would simply
act as a constant amplifier of the t-BuOH product.
One set of circumstances that would generate a qualitatively correct pressure dependence as a result of secondary radical chemistry would be a pressure-dependent
termination rate. This could result if the chain termination rate were limited by diffusion from the photolysis
region of the cell to the cell walls. The hypothesis is
that as pressure increases, fewer t-BuO' are produced
by laser photolysis, but diffusion of t-BuOO· to the
walls takes longer. This allows the chain propagation
step (R8) to continue producing secondary t-BuO·. The
pressure dependence of the rate of production of t-BuOH
then would depend on the balance between t-BuOH produced from t-BuOO· via reaction (R8) and t-BuOH produced by t-BuOO~ dissociation. The ratio p of the
rates of production of t-BuOH from these two sources
is given by
_
kg[t-BuOO· F
p - k l k 2[hll ][t-BuOOH]/(k 2 + k 3[M]) •
(9)
In order to evaluate p, the steady-state concentration
of [t-BuOO' ] must be calculated.
At 200 Torr diffusion to the cell walls through a distance of 3 mm requires about 0.05 s_ In this time - 5
x 1012 t-BuOOH molecules are dissociated under typical
photolYSiS conditions, producing on the order of _ 1013
t-BuOO' radicals. Substituting this steady-state concentration into Eq. (8), and using the value of kg = 1
X 103 S-1 1{"132 results in a value for p of -10- 7• The
conclusion is that the rate of production of t-BuOH via
photodissociation is seven orders of magnitude greater
than the rate of production of t-BuOH via reaction (R8)
assuming the chain is terminated by diffusion to the
walls. A chain length controlled by diffusion clearly
cannot account for the observed pressure dependence.
Of course, there is no information that directly implies
wall termination in these experiments. So chain mechanisms in which the pressure dependence arises from
some other type of termination step cannot be ruled out
unequivocally.
Nevertheless, any contribution to the total yield of
t-BuOH from pressure-dependent secondary chemistry
of the t-BuOO· radical appears doubtful based on the
following two experiments:
(1) PhotolYSiS of t-BuOOH vapor at 325.0 nm using
a 3 mW He-Cd laser gives an almost pressure-independent yield of t-BuOH. Dissociation from this excited
state proceeds with a quantum yield of unity, even in
2g
solution.
Laser power was chosen to give t-BuOH
4455
production rates comparable to the overtone experiments. Under these conditions, the excited precursor
to the primary radicals cannot be quenched. Hence,
observation of pressure-dependent t-BuOH production
rates in this experiment would imply that secondary
sources of alcohol could be pressure sensitive. In contrast, very little pressure effect is observed. At 200
Torr there is a 10% increase in the yield of t-BuOH
above that obtained at 7 Torr. This increase is expected from consideration of the pressure dependence
of the branching ratio of the highly excited t-BuO· ,
produced from dissociation of the prepared electronic
state, into either acetone or t-BuOH, according to reactions (R4) and (R7), and is in any case much smaller
than would be required to rationalize the overtone data.
(2) Addition of radical quenchers leads to no change
in the observed t-BuOH yield. At 1, 4-cyclohexadiene
concentrations three times as great as that of t-BuOOH,
1, 4-cyclohexadienyl should replace t-BuOO· as the
dominant radical species:
t-BuOO·
+
0 ':.:
t-BuOOH
+
0
(R9)
This reaction is 17 kcal/mol exothermic 31 and would be
predicted to occur at a rate that would dominate reaction (R8). The relative rates of reactions (R8) and (R9)
are calculated to be - 10-3 and 102, respectively, for 7
Torr total pressure, using the k9 value 8 x 101 1{"1 S-I. 33
Since negligible change in the apparent t-BuOH production rate occurs under these conditions, secondary
sources of t-BuOH ariSing from reaction (R8) are highly
unlikely.
Table III summarizes the reactions pertinent to the
fate of t-BuOO· radicals. From the above it is concluded that postdissociation radical chemistry cannot
explain the deviation of t-BuOH production from linearity at high pressure.
D. Kinetic scheme based on a combination of
nonstatistical and statistical unimolecular decomposition
If there are two excited precursors that lead to primary radicals, one dissociating at a fast rate, such
that it is unquenched by collisions, and the other at the
previously discussed RRKM rate, then all the data of
Fig. 6 can be rationalized. The simple kinetic scheme
(R1)-(R6) is modified to include a fast precursor by replacing reaction (R1) with the following "Rabinovitchlike" decomposition mechanism:
t-BuOOH + hll ~ t-BuOOHtt ,
(R10)
t-BuOO~t ~ t-BuO. +. OH ,
(Rll)
t-BuOOHtt ~ t-BuOOHt .
(R12)
Here t-BuOOHtt represents a vibrationally excited tBuOOH molecule whose energy distribution is not totally
randomized. This species can relax to a randomized
t-BuOOHt via reaction (R12). At low pressures, reaction (R2) is the principal source of product, and the
pressure dependence conforms with that suggested by
the Simple kinetic scheme (R1)-(R6). However, reac-
J. Chern. Phys., Vol. 77, No.9, 1 November 1982
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4456
Chandler, Farneth, and Zare: Mode-selective chemistry
TABLE III. Chemistry of the terl-butylperoxyl radical at 300 K.
AHo
(kcal/mol)
Reaction
k (s-I)a
Literature
source
(1) 2t-BuOO.-2t-BuO.+O:!
-4.8
_10- 5
Reference 32
(2) t-BuOO-+t-BuOOH-t-BuOOH+t-BuOOH
+9
_10- 7
Reference 33
_10 2
(3) t-BuOO. -walls
(4) t-BUOO'+O-t-BUOOH+O
3 x 10-2
-17
Reference 33
aFor (1) a steady state concentration of t-BuOO' = 1 x 10-8 M is used, see the text. For (2) and
(4) 7 Torr of H atom donor is used. For (3) we use a 0.3 cm path length at 7 Torr pressure.
tion (Rll) becomes an increasingly important source of
product at higher pressures as collisional quenching
[reaction (R3)] overtakes dissociation of the energyrandomized t-BuooIf via reaction (R2). Furthermore,
the initial precursor t-BuooIf.t is capable of displaying
different pressure-dependent behavior than t-BuOOHt
since energy distribution as well as energy content will
influence the dissociation rates. When reactions (Rl0)(R12) is incorporated into the kinetic scheme, kapp is
no longer described by Eq. (8) but instead by the relation
kapp = k 10
x (
i:hv [(k2(E~2iE1s[M])
k12 ) + ku ]f(E) dE •
kl1 + k12
kl1 + k12
(10)
Here k l1 /(k l1 + k 12 ) is the fraction of excited molecules
that dissociate via reaction (Rll) and is experimentally
determined, [k 2(E)/(k 2(E) + k3r Mnlr k 12/(k l1 + k 12 ) 1the
fraction that dissociates via reaction (R2), and [ks[M]!
(k 2(E) + ks[M]) ][k 12 /(k l1 + kd] the fraction that is collisionally deactivated.
The solid curve of Fig. 6 shows the fit of Eq. (10)
assuming k 10 = kl obtained earlier from Eq. (8). The
high pressure asymptote of our data (Fig. 6) determines
the value of k l1 /(k l1 + kd. Although both kl1 and k12 are
energy dependent, only the average ratio k l1 /(k u + k 12 )
is determined and this fraction is treated as a constant
in the integration of Eq. (10). This treatment gives a
very acceptable description of the form of the pressure
dependence of k~p at all pressures studied.
The ratio of the high pressure limiting value of k~p
to the zero pressure intercept yields the fraction of excited molecules that react before energy randomization
ku/(ku + kd. Values for the zero pressure intercept
are available from three sources: (1) by linear extrapolation of the low-pressure data [(k;;p)o~ 2.0]; (2) from
the value of klO for the best fit theoretical curve of Eq.
(10) [(k;:p)o ~ o. 05]; (3) by calculation of the number of
excited molecules per unit time from measured values
of the absorption cross section and intracavity photon
density [(k~p)o= O. 35]. The extrapolation of the lowpressure data gives a value too large because even in
the low-pressure region where the statistical decomposition rate [the first term of Eq. (10)] dominates, k;;p
is expected to be nonlinear in pressure. This is the
lesson of Eq. (8) and results from the finite width of the
energy distribution of photoexcited molecules. In addition, increased branching of t-BuO· to acetone at the
expense of t-BuOH contributes to a nonlinear increase
in rate at low pressures. The factor of 7 difference between the calculated intercept (0.35) and the theoretical
fit (0.05) is somewhat more puzzling. However, we are
reluctant to attach any Significance to this difference due
to the difficulty in calculating the intercept accurately,
and assumptions inherent in the theoretical fit. For example, either weak collision effects, or an energy distribution function that is skewed toward higher energies
than the assumed Maxwell-Boltzmann function (due perhaps to enhanced absorption cross section of some hot
bands) would give better agreement as would relatively
small changes in the t-BuOOH dissociation energy used
in the RRKM calculations. Errors in the measured absorption cross section or the calibration data could
easily amount to a factor of 2 or 3.
The uncertainties inherent in the determination of klO
from the fit seem greater than those of the calculation.
Therefore where a value for klO is required in the following paragraphs the calculated intercept of 0.35 will
be used.
At 160 Torr, the data shows that production of t-BuOH
is essentially pressure independent. The ratio of this
high pressure limit to the intercept gives k ll /(k ll + k 10 )
~ 10-2 • It is the consensus of previous work both experimenta19 ,S4,S5 and theoreticals6 that rate constants for
energy redistribution in highly vibrationally excited
poly atomics k12 will be on the order of lOu _l013 S-l. In
combination, these numbers suggest a rate constant for
the unimolecular decay of the nonrandomly activated
molecule of the order of 1010 s-l.
This limit for kl1 can be rationalized by an RRKM
rate constant, using identical values of reaction threshold and total energy but assuming that the energy is
shared only within a portion of the molecule, called a
"part molecule."s If the part molecule is chosen to include all oscillators except those involving C-H and
CH2 motions, the calculated unimolecular rate constant
at E for the distribution in Fig. 8 is ku (E) = 3 x 109 S-1.
If the part molecule is selected to be only the C-O-O-H
moiety the calculated rate would be on the order of 1011
S-l. These estimates serve to show that the fitting of
the data to the proposed Rabinovitch-like mechanism
provides reasonable limits for ku and k12' i. e., the
pressure-dependent decomposition rate of photoactivated
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Chandler, Farneth, and Zare: Mode-selective chemistry
t-BuCX)H can be satisfactorily explained by invoking a
kinetic scheme involving dissociation from precursors
having both nonrandomized and randomized vibrational
energy distributions.
E. Other possible kinetic schemes
It is clear that any mechanism that produces a constant t-BuOH yield of -1% of photoexcited t-Bu()(>H independent of pressure will be successful in fitting the
high-pressure data of Fig. 6. In this section, four possible schemes are presented which could contribute to
the observed t-BuOH production:
(1) The possibility exists that bUlk heating of the sample due to laser absorption could lead to thermal disSOCiation of t-BuOOH. However, it is unlikely that this
mechanism contributes Significant amounts of t-BuOH.
Experiments at a constant total pressure and different
t-BuOOH partial pressures (1 and 7 Torr), and therefore different amounts of heating, give identical results.
(2) Coherent absorption of two photons would place
the t-BuOOH into an electronic state whose dissociation
would be rapid on the collisional timescale. To test for
the likelihood of this, a power dependence of the i-BuOH
production was carried out at the highest pressure (160
Torr). When the laser power is varied by a factor of 2
a linear power dependence is observed indicating that a
coherent two-photon effect is not responsible for the observed rates.
(3) A particularly troublesome possibility is that of
a laser-induced reaction at the windows of the cell.
Tert-BuOOH absorbed on to the Windows may dissociate
mOre efficiently than gas-phase t-BuOOH. Two observations are made which argue against this mechanism
being responsible for the shape of the high-pressure
data of Fig. 6. The first is that the data are very consistent from one run to the next on the same sample as
well as from one experiment to the next. Other experimenters who have seen window effects have noted their
irreproducibility. 37 The second observation is that the
dissociation rate follows the shape of the gas-phase absorption curve while that of t-BuOOH adsorbed on the
windows would most likely be substantially broadened
and red shifted.
(4) It is well established that collisions not only deactivate excited molecules but can also further activate
them. 1,38 The question arises: What is the possibility
that a few collisions add sufficient energy to 1% of the
t-BuOOHt in order to increase the reaction rate enough
to explain the results. A reaction rate on the order of
10 9 8-1 is needed. Examination of Fig. 8 shows that in
order to obtain an RRKM rate of this magnitude the tBuOOHt would have to obtain through collisions - 8000
cm-1 energy above E. Since the typical collision partner
(SF 6) has an average::s; 1000 cm- 1 of energy to contribute
at least four successive energy-contributing collisions
would be necessary to explain our observed rate, a
highly unlikely scenerio for such large poly atomics at
rOOm temperature. This scenerio would also predict a
large distribution of reaction rates while the data is
very adequately modeled with only a convolution of two
rates, the RRKM rate, as obtained in Sec. B, and a
4457
rate significantly faster than our collisional rate.
As is characteristic of kinetic studies, one is only able
to find schemes that are consistent with observations
but consistency is not a demonstration of uniqueness.
Many controls were performed to check for experimental artifacts. Nevertheless, the possibility of some undiscovered source of laser-produced t-BuOH at high
pressures still remains. The proposed scheme is
recommended not only by its consistency with the experimental observation, but also by its precedent in
similar chemical activation experiments. The proposed
mechanism (R2)-(R12) suggests several additional experiments that are worth pursuing. One is that the
fraction k ll /(k l1 + k t2 ) of photoactivated t-BuOO~t that
diSSOciates prior to energy randomization will increase
with increasing excitation of the O-H overtone. Another is that excitation into the C-H overtone should
produce t-BuOOHtt with a different ku/(ku + k 12 ) ratio.
In particular, it is anticipated that C-H overtone excitation should exhibit a linear pressure dependence to
much higher total pressures than O-H overtone excitation. While such an experimental study is very difficult
for t-BuOOH because of the weakness of the C-H overtones compared to the rate of background reaction, this
pOint might be investigated using other molecular systems.
Finally, it should be noted that the possibility of
mode-specific chemistry is definitely indicated by this
work, since a small fraction (-1%) of the photoexcited
molecules appear to decompose from nonstatistically
prepared precursors. Deviations from RRKM behavior
in the unimolecular decomposition of t-BuOOH might be
studied by direct detection of the prOducts 5 but on a ps
time scale. Another such means is to use collisional
deactivation as a clock to achieve the same effective
timescale, as done here. Although the quantum yields
from energy nonrandomized molecules may be quite
small, this further suggests that under certain circumstances these effects might be most apparent in condensed media.
ACKNOWLEDGMENTS
W. E. Farneth would like to thank the University of
Minnesota for support during his quarter leave. He
would like to acknowledge the support of the Department
of Energy, Grant AC02-80ER-10592. D. W. Chandler
and R. N. Zare would like to acknowledge the support
of the National Science Foundation under Grant NSF
CHE 80-06524. R. N. Z. thanks the Shell Companies
Foundation, Inc., for support through the Shell Distinguished Chairs Program.
APPENDIX A: PARAMETERS FOR RRKM
CALCULATIONS
RRKM rate constants for the unimolecular decomposition of t-butylhydroperoxide were calculated using
Eq. (A1)1:
t
k (E*) _ L~Q; L:;t.oP(Eh)
•
- hQ1
N*(E*)
,
(A1)
= reaction path degeneracy = 1, (QI/Q,) = ratio of
adiabatic partition functions = 1. 25, 39 &~LDP(Et R) = sum
L*
J. Chern. Phys., Vol. 77, No.9, 1 November 1982
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4458
Chandler, Farneth, and Zare: Mode-selective chemistry
of vibrational states of activated complex from Eo to
Eo+Et, and N*(E*) =density of vibrational states of reactant at energy E*. State sums and densities were calculated using the algorithm described in Ref. 26. All
internal degrees of freedom were assumed to be harmonic oscillators. Frequencies were chosen in accord
with previous RRKM calculations on di-t-butylperoxide 21
for the oscillators that these molecules share, and O-H
stretching, and O-O-H bending frequencies were estimated. Activated complex frequencies were obtained
by lowering the 0-0 rotation barrier and reducing the
0-0 stretch and the C-C-O, C-O-O, and O-O-H bending frequencies to fit the known thermal A factor .13 Eo
was taken as 40.7 kcal/mol (14270 cm- 1) (E ~ = 42.2 kcal/
mol).13 The calculated value of k., (500°C) using these
parameters agrees exactly with that obtained from the
measured Arrhenius parameters. 13 The actual frequencies used (and their degeneracies) are listed below:
t-BuOOH-3200, 2960(9), 1425(9), 1256(3), 1031(3),
940(4), 914, 523(2), 444(2), 268(3), 178(3), 50(2).
Activated complex-3200, 2960(9), 1425(9), 1256(3),
1031(3), 940(4), 523, 444(2), 268(2), 178(2), 85(3),
50, 10.
lp. J. Robinson and K. A. Holbrook, Unimolecular Reactions
(Wiley-Interscience, New York, 1972), and references therein.
2(a) E. K. Gill and K. J. Laidler, Proc. R. Soc. London Ser.
A 250, 121 (1959); (b) D. L. Spicer and B. S. Rabinovitch,
Annu. Rev. Phys. Chern. 21, 349 (1970).
31. Oref and B. S. Rabinovitch, Acc. Chern. Res. 12, 166
(1979).
4H• Hippler, K. Luther, J. Troe, and R. Walsh, J. Chern.
Phys. 68, 323 (1979).
5T. R. Rizzo and F. F. Crirn, J. Chern. Phys. 76, 2754
(1982).
SA. -N. Ko and B. S. Rabinovitch, Chern. Phys. 30, 361
(1978).
7J • F. Meagher, K. J. Chao, J. R. Barker, and B. S.
Rabinovitch, J. Phys. Chern. 78, 2535 (1974).
8F • C. Wolters, B. S. Rabinovitch, andA.-N. Ko, Chern.
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(1972) .
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19Halocarbon wax is available from Halocarbon Products Corp. ,
82 Burlews Court, Hackensack, N. J.
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23J • O. Hirschfelder, C. F. Curtis, and R. B. Bird, The
Molecular Theory of Gases and Liquids (Wiley, New York,
1976).
24We have used the frequencies suggested in Ref. 10 for dit-butyl peroxide for the oscillators that these molecules
share, and add O-H stretching and O-O-H bending frequenCies.
The activated complex frequencies were obtained by lowering the 0-0 rotation barrier to zero and reducing the 0-0
stretch, and C-C-O, C-O-O, and O-O-H bending frequenCies
to fit the known A factor.
25S. W. BensonandG.N. Spokes, J. Phys. Chern. 72,1182
(1972), k., at T=500 K.
2SS. E. Stein and B. S. Rabinovitch, J. Chern. Phys. 58,2438
(1973).
27R. Hiatt and K. C. Irwin, J. Org. Chern. 33, 1436 (1968);
R. Hiatt, T. Mill, K. C. Irwin, and J. K. Castleman, J.
Org. Chern. 33, 1421 (1968).
28J. T. Martin and R. G. W. Norrish, Proc. R. Soc. London
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30H. Paul, R. D. Small, Jr., and J. C. Scaiano, J. Am.
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31S. W. Benson, Thermochemical Kinetics, 2nd ed. (Wiley,
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32J. A. Howard, in Advances in Free Radical Chemistry, Vol.
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